Linear response and moderate deviations: hierarchical approach. IV

TL;DR

This paper extends the Moderate Deviations Principle to splittable random fields integrated against test functions, advancing understanding in the context of dependent random structures.

Contribution

It establishes the MDP for splittable random fields, a case previously not well-understood, using a hierarchical approach.

Findings

MDP proven for splittable random fields

Enhanced understanding of moderate deviations in dependent structures

Methodology applicable to complex random fields

Abstract

The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random fields integrated against test functions. Version 2: minor changes. Interval [0,1] replaced with [0,1) for better compatibility with Part V. Copyedit pages 3, 4, 6, 16, 22, 23.